Historically, potentiometric titration was the standard method for pKa measurement. In a potentiometric titration, a sample is titrated with acid or base using a pH electrode to monitor the course of titration. The equivalence point is the volume at which the slope is greatest, or at which the inflection point occurs, where the line changes from upward curvature to downward curvature.
The pKa value is calculated from the change in shape of the titration curve compared with that of a blank titration, i.e. without a sample present. Potentiometric titration is a high-precision technique for determining the pKa values of substances. It is commonly used due to its accuracy and the commercial availability of fast, automated instruments. However, the shortcomings of the method include the requirements to use a milligram of pure compounds and a mixture of aqueous buffers. Solutions of at least 10-4 M are required in order to detect a significant change in shape of the titration curve. To avoid errors, especially for measurements at neutral-to-high pH, carbonate-free solutions must be prepared (Babic et al, 2007). Although potentiometric titration of sparingly soluble compounds may be done in the presence of co-solvents such as methanol, the resulting acid dissociation constants refers only to the particular solvent medium employed, and extrapolation procedures, such as the Yasuda-Shedlovsky method, are required to deduce the pKa values at zero co-solvent (Takács-Novák et al, 1997).
UV-Vis spectrophotometry is used to study the dissociation of weak electrolytes. UV–VIS spectrophotometry can handle compounds with lower solubility and lower sample concentrations compared to titration methods. The main advantage is higher sensitivity (> 10-6 M) to compounds with favourable molar absorption coefficients. However, in such a case, a compound must contain a UV-active chromophore close enough to the site of the acid–base function in the molecule. Spectral data are recorded continuously during the course of titration by a spectrometer. The absorption spectra of the sample changes during the course of the titration to reflect the concentration of neutral and ionised species present. The largest change in absorbance occurs at the pH corresponding to a pKa value. These changes are usually identified from the first derivative of the absorbance against time plot or from overlay plots of the different spectra.
The determination of pKa values by UV–VIS assumes that the solute of interest is pure or that its impurities do not absorb in the UV–VIS range, since the spectra of impurities can overlap with those corresponding to the solutes of interest. Spectrophotometric methods offer excellent precision, as in potentiometry, but they require different spectra for different species at experimentally suitable wavelengths (generally above 220 nm). Traditionally, spectral data at a single analytical wavelength are acquired from a sample in a series of buffer solutions with known pH values, after which the pKa is determined. To use this method, the absorption spectra of individual species must be characterised beforehand and the molar absorptivities of protonated and deprotonated species are thus required. These measurements are non-trivial if acid-base equilibria comprise more than two ionisation steps or if reacting components are not stable within two pH units of the pKa value, so a multi-wavelength spectrophotometric approach has been developed to determine acid dissociation. Target-factor analysis has been applied to deduce pKa values from the multiwavelength UV absorption data recorded at different pH values (Allen et al, 1998; Babic et al, 2007). The method is suited for compounds with either very high or very low pKa values.
Since the conductance of a solution of is a measure of the concentration of H+ and A- ions, a measurement of conductance of a solution of known [HA] concentration allows to calculate the degree of dissociation of the compound (dissociated fraction = ƒ¿) as the ratio of molar electric conductivity at a given concentration (ƒ©c) to the maximum molar electric conductivity (ƒ©‡).
The conductometric method is applied by measuring the conductivity of a 0.1 M solution of the test substance in distilled water, followed by measurements on a series of sequentially diluted solutions. The equivalent conductance is calculated for each acid concentration and for each concentration of a mixture of one equivalent of acid, plus 0.98 equivalents of sodium hydroxide. Values of 1/ƒ©c are plotted against ãC and ƒ©‡ (Kohlrausch law: ƒ©=ƒ©‡ .a ãC, where ƒ©‡: equivalent conductance at infinite dilution, c: concentration; a: constant). The pKa can be calculated from ƒ¿ = ƒ©c/ƒ©‡ and Ka = ƒ¿2 /(1-ƒ¿).
The conductivity of a solution is dependent on several factors, including the concentration of the solute, the degree of dissociation of the solute, the valence of the ion(s) present in the solution, the temperature, and the mobility of the ions in the solution.
Since the charge of ions in solution facilitates the conductance of electrical current, the conductivity of a solution is proportional to its ion concentration. In some situations, however, conductivity may not correlate directly to concentration. For strong electrolytes, such as salts and strong acids and bases, molar conductivity varies little with concentration, but for weak electrolytes, such as weak acids, molar conductivity depends strongly on concentration, being exponentially smaller with smaller concentration. Molar conductivity or equivalent conductance of a solution changes with the concentration of the solution:
In practice this method is more laborious than the potentiometric method and more calculations are needed. The method is especially suited for acids with pKa values between 1.9 and 5.2. It is less reliable in the study of very weak electrolytes; i.e. very high pKa values.